Simultaneous wing shape and actuator parameter optimization using the adjoint method

Abstract

Increasing attention to urban air mobility with distributed electric propulsion causes an increased interest in propeller aircraft design and optimization. Various studies have focused on designing and optimizing the aerodynamic performance of wings and propellers. However, existing studies optimized the wing and propeller separately due to the numerical challenges in simulations and optimization. It is not clear to what extent high-fidelity coupled wing-propeller aerodynamic optimization can benefit the propeller aircraft design. As a first step to answer the above question, this study develops the capability to simultaneously optimize the wing shape and actuator parameters. We use a high-fidelity computational fluid dynamics solver to simulate the wing aerodynamics, and the propeller is modeled as an actuator disk. We develop a smoothed actuator disk formulation that allows us to change the actuator's location and radius during the optimization, along with the wing shape. We use the discrete adjoint approach to compute the derivatives and couple them with a gradient-based optimization framework. The benefit of the above adjoint-based optimization framework is that it can use a large number of design variables to allow large design freedom for both wing and actuator. We perform 15 optimizations to evaluate how various actuator parameters impact the wing aerodynamic performance; both single and double actuator configurations are considered. We observe that the spanwise location and outer radius are the two most important actuator parameters, and using more actuator parameters as the design variables result in better performance. For example, optimizing the wing shape while allowing the actuator location and outer radius to move exhibits 11.4% more drag reduction compared with optimizing the wing shape while fixing the actuator parameters. This study serves as the starting point for more detailed high-fidelity coupled wing-propeller aerodynamic optimizations.